Data

Tools

Indexes

Applications

Experiments

Awesome

An open API service indexing awesome lists of open source software.

https://github.com/joselado/quantum-lattice

User-friendly open-source software to design and solve tight-binding models, addressing electronic properties, topology, interactions, non-collinear magnetism, and unconventional superconductivity, among others.
https://github.com/joselado/quantum-lattice

interactions mean-field-theory spin-orbit-coupling superconductivity tight-binding topological-insulator topology user-interface

Last synced: about 2 months ago
JSON representation

User-friendly open-source software to design and solve tight-binding models, addressing electronic properties, topology, interactions, non-collinear magnetism, and unconventional superconductivity, among others.

Awesome Lists containing this project

README 

          
## QUANTUM LATTICE ##



# Summary #



This program allows to perform tight binding calculations with a user friendly interface in a variety of lattices and dimensionalities.



![Alt text](screenshots/quantum_lattice.png?raw=true "Quantum Lattice System selection")



# Video examples #



[Here](https://youtu.be/g2YAE9Kpd9c) 

you can see four simultaneous examples of the

usage of Quantum Lattice.



Below you can see videos showing the real-time usage of this program for

individual examples

- [Confined modes in graphene nanoislands](https://youtu.be/YFIpONVQinc)

- [Superlattices](https://youtu.be/cPx2tOFxdyI)

- [Interaction-induced magnetism](https://youtu.be/RrPWVqJ7VS4)

- [Artificial Chern insulators](https://youtu.be/zEwywwQprNY)

- [Landau levels and quantum Hall edge states](https://youtu.be/aI-2rMdZ8iY)

- [Twisted bilayer graphene](https://youtu.be/OHlLOLKAfVs)



# How to install #



## Linux and Mac ##



The program runs in Linux and Mac machines. 



Clone the GitHub repository

```bash

git clone https://github.com/joselado/quantum-lattice

```



and execute the script install as

```bash

python install.py

```



The script will install all the required dependencies if they are not already

present for the python command used. Afterwards, you can run the program by 

executing in a terminal



```bash

quantum-lattice

```



You can see [here](https://youtu.be/4H1mNLYdUOU) a short video demonstrating the installation.



## Windows ##



For using this program in Windows, the easiest solution is to create a virtual

machine using [Virtual Box](https://www.virtualbox.org/), installing

a version of [Ubuntu](https://releases.ubuntu.com/20.04/) 

in that virtual machine, and following the previous

instructions. 



# FUNCTIONALITIES #

## Single particle Hamiltonians ##

- Spinless, spinful and Nambu basis for orbitals

- Full non-collinear electron and Nambu formalism

- Include magnetism, spin-orbit coupling and superconductivity

- Band structures with state-resolved expectation values

- Momentum-resolved spectral functions

- Local and full operator-resolved density of states

- 0d, 1d, 2d and 3d tight binding models



## Interacting mean-field Hamiltonians ##

- Selfconsistent mean-field calculations with local/non-local interactions

- Both collinear and non-collinear formalism

- Anomalous mean-field for non-collinear superconductors

- Full selfconsistency with all Wick terms for non-collinear superconductors

- Automatic identification of order parameters for symmetry broken states



## Topological characterization ##

- Berry phases, Berry curvatures, Chern numbers and Z2 invariants

- Operator-resolved Chern numbers and Berry density



## Spectral functions ##

- Surface spectral functions for semi-infinite systems

- Single impurities in infinite systems

- Operator-resolved spectral functions



## Chebyshev kernel polynomial based-algorithms ##

- Local and full spectral functions

- Operator resolved spectral functions

- Reaching system sizes up to 1000000 atoms on a single-core laptop



Quantum Lattice uses [pyqula](https://github.com/joselado/pyqula).



# Screenshot examples #



## Unconventional superconductivity ##

Electronic band structure, Berry curvature and momentum resolved surface

spectral function of a px + ipy spin-triplet topological

superconductor with d-vector (0,0,1).

![Alt text](screenshots/chiral_superconductor.png?raw=true "Spin-triplet chiral topological superconductor")



## Interaction-driven non-collinear magnetism ##

Electronic band structure and selfconsistent local magnetization

of a square lattice with an applied Zeeman field

and local Hubbard interactions.

![Alt text](screenshots/non_collinear_scf.png?raw=true "Non-collinear magnetization with Hubbard interactions and Zeeman field")



## Superlattices ##

Electronic band structure, Fermi surface and local density of states

of a superlattice built from a defective triangular lattice

![Alt text](screenshots/2d_superlattice.png?raw=true "Triangular superlattice")



## Scanning tunnel spectroscopy of nanographene islands ##

Real space simulation of the STS spectra, using atomic-like orbitals

for a nanographene island

![Alt text](screenshots/nanographene.png?raw=true "STS nanographene")



## Kagome lattice with first and second neighbor hopping ##

Fermi surface and band structure of a two-dimensional lattice,

including both first and second neighbor hoppings. In the absence

of second neighbor hopping, the lowest band is flat. Only first

neighbor hoppings are shown in the 3D structure plot.

![Alt text](screenshots/kagome_lattice_second.png?raw=true "Kagome lattice with NN and NNN hopping")



## Interaction-induced symmetry breaking in the Lieb lattice ##

Non-interacting and interacting band structure of a two-dimensional

Lieb lattice. When repulsive 

local Hubbard interactions are included, an spontaneously

ferromagnetic state appears in the system, leading to a real-space

magnetic distribution.

![Alt text](screenshots/lieb_scf.png?raw=true "Interacting Lieb lattice")



## Artificial Chern insulators ##

Kagome lattice with Rashba spin-orbit coupling and exchange field, giving rise to a net Chern number and chiral edge states

![Alt text](screenshots/qah.png?raw=true "QAH state in the Kagome lattice")



## Two-dimensional quantum Spin Hall state ##

Honeycomb lattice with Kane-Mele spin-orbit coupling and Rashba spin-orbit coupling, giving rise to a gapped spectra with a non-trivial Z2 invariant and helical edge states https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.226801

![Alt text](screenshots/qsh.png?raw=true "QSH state")



## Magnetism in graphene zigzag nanoribbons ##

Self-consistent mean field calculation of a zigzag graphene ribbon, with electronic interactions included as a mean field Hubbard model. Interactions give rise to an edge magnetization in the ribbon, with an antiferromagnetic alignment between edges

![Alt text](screenshots/zzscf.png?raw=true "Magnetism in zigzag nanoribbons")



## Three-dimensional quantum spin Hall insulators ##

Three-dimensional quantum spin-Hall insulator, engineered by intrinsic

spin-orbit coupling in the diamond lattice. the top and bottom of the

slab show an emergent helical electron gas.

![Alt text](screenshots/3D_QSL.png?raw=true "3D QSH state")



## Scanning tunnel spectroscopy of graphene nanoribbons ##

Real space simulation of the STS spectra, using atomic-like orbitals

for a graphene nanoribbon 

![Alt text](screenshots/sts_nanoribbon.png?raw=true "STS graphene nanoribbon")



## Nodal line semimetals ##

Band structure of a slab of a 3D nodal line semimetal in a diamond lattice, showing the emergence of topological zero energy drumhead states in the surface of the slab https://link.springer.com/article/10.1007%2Fs10909-017-1846-3

![Alt text](screenshots/nodalline.png?raw=true "Magnetism in zigzag nanoribbons")



## Confined modes in quantum dots ##

Spectra and spatially resolved density of states of square quantum dot, showing the emergence of confined modes

![Alt text](screenshots/island.png?raw=true "Confined modes in square quantum dot")



## Colossal quantum dots ##

Density of states and spatially resolved density of states of a big graphene quantum dot. The huge islands module uses special techniques to efficiently solve systems with hundreds of thousands of atoms.

![Alt text](screenshots/giant_island.png?raw=true "Big graphene island")



## Landau levels ##

Electronic spectra of a graphene lattice in the presence of an off-plane magnetic field and antiferromagnetic order, giving rise to Landau levels and chiral edge states

![Alt text](screenshots/honeycomb_qh.png?raw=true "Landau levels in an antiferromagnetic graphene ribbon")



## Artificial topological superconductors ##

Bogoliuvov de Gennes band structure of a two-dimensional gas in a square lattice with Rashba spin-orbit coupling, off-plane exchange field and s-wave superconducting proximity effect. When superconductivity is turned on, a gap opens up in the spectra hosting a non-trivial Chern number, giving rise to propagating Majorana modes in the system

![Alt text](screenshots/topologicalSC.png?raw=true "Artificial topological superconductor in a square lattice")



## Quantum Valley Hall effect ##

Band structure of Bernal stacked bilayer graphene, showing the emergence of a gap when an interlayer bias is applied. The previous gap hosts a non-trivial valley Chern number, giving rise to the emergence of pseudo-helical states in the edge of the system

![Alt text](screenshots/qvh.png?raw=true "Quantum valley Hall state in biased bilayer AB graphene")



## Twisted bilayer graphene ##

Bandstructure and Fermi surface of a twisted graphene bilayer, showing the emergence of nearly flat bands

https://journals.aps.org/prb/abstract/10.1103/PhysRevB.82.121407

![Alt text](screenshots/tbg.png?raw=true "Magic angle twisted bilayer graphene")



## Twisted trilayer graphene ##

Structure and band structure of a twisted graphene trilayer at the magic angle.

![Alt text](screenshots/TTG.png?raw=true "Twisted trilayer graphene")